Does the Bayesian MAP give a probability distribution over unseen t*?
You're correct: the MAP estimate is a point estimate (specifically, MAP is used to estimate the mode of a probability distribution).
I think that the paper is referring to the (output) probability distribution over the possible targets/labels, given the point estimate. However, in the case of MLE, you can also have that probability distribution, so I'm not sure why the paper's author is emphasizing that with MAP you can build that probability distribution (so maybe this/my interpretation of that excerpt is wrong!).
That table also shows that the MAP estimate is used to produce a probability distribution, but the $\sigma$ there should be unknown, but I didn't read that article, so maybe I am missing some info or assumption.
In any case, you could also find a point estimate of a parameter of a probability distribution, but this does not imply that MAP produces a probability distribution. For instance, you can show that, if you place a Gaussian prior on the weights of a neural network, this leads to the $L_2$ loss function, but training a (normal) neural network with $L_2$ does not lead to a probability distribution over the weights.
You should try reading only information from reliable references and books. For MAP, check out chapter 5. (p. 149) of the book &quot;Machine Learning: A Probabilistic Perspective&quot; by Murphy.